• Journal of the Korean Statistical Society
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• 제32권3호
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• pp.271-288
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• 2003

In this paper, when the variance of the normal distribution is related to the mean, we develop noninformative priors such as matching priors and reference priors. We prove that the second order matching prior matches alternative coverage probabilities up to the same order and also it is a HPD matching prior. It turns out that one-at-a-time reference prior satisfies a second order matching criterion. Then using these noninformative priors, we develop a Bayesian test procedure for the equality of the means and variances of two independent normal distributions using fractional Bayes factor. Some simulation study is performed, and a real data example is also provided.

• Journal of the Korean Data and Information Science Society
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• 제27권2호
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• pp.565-575
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• 2016

In this paper, we develop the noninformative priors for the linear combinations of means in the exponential distributions. We develop the matching priors and the reference priors. The matching priors, the reference prior and Jeffreys' prior for the linear combinations of means are developed. It turns out that the reference prior and Jeffreys' prior are not a matching prior. We show that the proposed matching prior matches the target coverage probabilities much more accurately than the reference prior and Jeffreys' prior in a frequentist sense through simulation study, and an example based on real data is given.

• Journal of the Korean Data and Information Science Society
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• 제21권5호
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• pp.935-944
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• 2010

In this paper, we develop the noninformative priors for the reliability in a stress-strength model where a strength X and a stress Y have independent exponential distributions with different scale parameters and a common location parameter. We derive the reference priors and prove the propriety of joint posterior distribution under the general prior including the reference priors. Through the simulation study, we show that the proposed reference priors match the target coverage probabilities in a frequentist sense.

• 한국산업정보학회:학술대회논문집
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• 한국산업정보학회 2009년도 춘계학술대회 미래 IT융합기술 및 전략
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• pp.107-113
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• 2009

This paper deals with noninformative priors for such as Jeffres' prior, reference prior and probability matching prior for scale parameter of exponential distribution when the data are collected in multiple step stress accelerated life tests. We find the noninformative priors for this model and show that the reference prior satisfies first order matching criterion. Using artificial data, we perform Bayesian analysis for proposed priors.

• Journal of the Korean Data and Information Science Society
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• 제22권1호
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• pp.115-123
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• 2011

In this paper, we develop the noninformative priors for stress-strength reliability from the Pareto distributions. We develop the matching priors and the reference priors. It turns out that the second order matching prior does not match the alternative coverage probabilities, and is not a highest posterior density matching or a cumelative distribution function matching priors. Also we reveal that the one-at-a-time reference prior and Jeffreys' prior are the second order matching prior. We show that the proposed reference prior matches the target coverage probabilities in a frequentist sense through simulation study, and an example is given.

• Communications for Statistical Applications and Methods
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• 제18권4호
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• pp.467-475
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• 2011

This paper develops the noninformative priors for the stress-strength reliability from one parameter generalized exponential distributions. When this reliability is a parameter of interest, we develop the first, second order matching priors, reference priors in its order of importance in parameters and Jeffreys' prior. We reveal that these probability matching priors are not the alternative coverage probability matching prior or a highest posterior density matching prior, a cumulative distribution function matching prior. In addition, we reveal that the one-at-a-time reference prior and Jeffreys' prior are actually a second order matching prior. We show that the proposed reference prior matches the target coverage probabilities in a frequentist sense through a simulation study and a provided example.

• Communications for Statistical Applications and Methods
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• 제9권3호
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• pp.835-844
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• 2002

For the one-way random model when the ratio of the variance components is of interest, Bayesian analysis is often appropriate. In this paper, we develop the noninformative priors for the ratio of the variance components under the balanced one-way random effect model. We reveal that the second order matching prior matches alternative coverage probabilities up to the second order (Mukerjee and Reid, 1999) and is a HPD(Highest Posterior Density) matching prior. It turns out that among all of the reference priors, the only one reference prior (one-at-a-time reference prior) satisfies a second order matching criterion. Finally we show that one-at-a-time reference prior produces confidence sets with expected length shorter than the other reference priors and Cox and Reid (1987) adjustment.

• Journal of the Korean Data and Information Science Society
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• 제27권3호
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• pp.835-844
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• 2016

We develop the testing procedures about the homogeneity of the shape parameters of several inverse Gaussian distributions in our paper. We propose default Bayesian testing procedures for the shape parameters under the reference priors. The Bayes factor based on the proper priors gives the successful results for Bayesian hypothesis testing. For the case of the lack of information, the noninformative priors such as Jereys' prior or the reference prior can be used. Jereys' prior or the reference prior involves the undefined constants in the computation of the Bayes factors. Therefore under the reference priors, we develop the Bayesian testing procedures with the intrinsic Bayes factors and the fractional Bayes factor. Simulation study for the performance of the developed testing procedures is given, and an example for illustration is given.

• Journal of the Korean Statistical Society
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• 제27권4호
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• pp.421-433
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• 1998

In this paper, matching priors for P(X < Y) are investigated when both distributions are exponential distributions. Two recent approaches for finding noninformative priors are introduced. The first one is the verger and Bernardo's forward and backward reference priors that maximizes the expected Kullback-Liebler Divergence between posterior and prior density. The second one is the matching prior identified by matching the one sided posterior credible interval with the frequentist's desired confidence level. The general forms of the second- order matching prior are presented so that the one sided posterior credible intervals agree with the frequentist's desired confidence levels up to O(n$^{-1}$ ). The frequentist coverage probabilities of confidence sets based on several noninformative priors are compared for small sample sizes via the Monte-Carlo simulation.

• Communications for Statistical Applications and Methods
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• 제12권2호
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• pp.395-411
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• 2005

In this paper, we develop the Jeffreys' prior, reference prior and the the probability matching priors for the difference of intraclass correlation coefficients in familial data. e prove the sufficient condition for propriety of posterior distributions. Using marginal posterior distributions under those noninformative priors, we compare posterior quantiles and frequentist coverage probability.